This study investigates changes in resting-state brain network structure in Alzheimer's disease (AD) patients compared to non-demented controls using graph theory. Magnetoencephalography (MEG) data from 18 AD patients and 18 controls were analyzed. The phase lag index (PLI), a measure of synchronization insensitive to volume conduction, was used to assess connectivity. AD patients showed reduced PLI in the lower alpha and beta bands, with decreased clustering coefficients and path lengths in the lower alpha band. These changes were better explained by a 'Targeted Attack' model than a 'Random Failure' model, suggesting that highly connected neural hubs are particularly vulnerable in AD. The study highlights a loss of resting-state functional connectivity in AD, even with PLI, and indicates that AD networks are more random. The findings support the concept of AD as a disconnection syndrome and suggest that network changes in AD are due to preferential loss of connections between high-degree nodes. The study also addresses the issue of volume conduction in EEG/MEG studies and shows that PLI is less affected by this. The results suggest that AD patients have altered network topology, with lower clustering coefficients and longer path lengths in the lower alpha band. The study underscores the importance of graph theory in understanding AD and other neurological disorders.This study investigates changes in resting-state brain network structure in Alzheimer's disease (AD) patients compared to non-demented controls using graph theory. Magnetoencephalography (MEG) data from 18 AD patients and 18 controls were analyzed. The phase lag index (PLI), a measure of synchronization insensitive to volume conduction, was used to assess connectivity. AD patients showed reduced PLI in the lower alpha and beta bands, with decreased clustering coefficients and path lengths in the lower alpha band. These changes were better explained by a 'Targeted Attack' model than a 'Random Failure' model, suggesting that highly connected neural hubs are particularly vulnerable in AD. The study highlights a loss of resting-state functional connectivity in AD, even with PLI, and indicates that AD networks are more random. The findings support the concept of AD as a disconnection syndrome and suggest that network changes in AD are due to preferential loss of connections between high-degree nodes. The study also addresses the issue of volume conduction in EEG/MEG studies and shows that PLI is less affected by this. The results suggest that AD patients have altered network topology, with lower clustering coefficients and longer path lengths in the lower alpha band. The study underscores the importance of graph theory in understanding AD and other neurological disorders.